math.AG — Algebraic Geometry

Serre’s conjecture on the Artin character for a regular local ring

Contributed by Mark Kisin

We prove Serre’s conjecture on the Artin character of a finite group G acting on a regular local ring A with isolated fixed points. The case of positive characteristic is due to Abe. In mixed characteristic we use an equivariant deformation to reduce to the case where A has an isolated singularity, in which case we can make use of the results of Beraldo and Pippi on the twisted conductor formula.